| Title |
On the non-closure under convolution for strong subexponential distributions |
| Authors |
Konstantinides, Dimitrios ; Leipus, Remigijus ; Šiaulys, Jonas |
| DOI |
10.15388/namc.2023.28.30208 |
| Full Text |
|
| Is Part of |
Nonlinear analysis: modelling and control.. Vilnius : Vilniaus universiteto leidykla. 2023, vol. 28, no. 1, p. 97-115.. ISSN 1392-5113. eISSN 2335-8963 |
| Keywords [eng] |
class of strong subexponential distributions ; class of subexponential distributions ; convolution closure |
| Abstract [eng] |
In this paper, we consider the convolution closure problem for the class of strong subexponential distributions, denoted as S*. First, we show that, if F, G ∈ L, then inclusions of F*G, FG, and pF + (1 – p)G for all (some) p ∈ (0; 1) into the class S* are equivalent. Then, using examples constructed by Klüppelberg and Villasenor [The full solution of the convolution closure problem for convolution-equivalent distributions, J. Math. Anal. Appl., 41:79–92, 1991], we show that S* is not closed under convolution. |
| Published |
Vilnius : Vilniaus universiteto leidykla |
| Type |
Journal article |
| Language |
English |
| Publication date |
2023 |
| CC license |
|
